Rank functions for closed and perfect \([0,1]\)-matroids. (English) Zbl 1213.05032
Summary: We present the notions of perfect \([0, 1]\)-matroid and closed \([0, 1]\)-matroid, and investigate some of their basic properties. Moreover, we prove that a closed and perfect \([0, 1]\)-matroid can be characterized by means of its \([0, 1]\)-fuzzy rank function.
MSC:
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 52B40 | Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) |
